## Bulletin of the Belgian Mathematical Society - Simon Stevin

- Bull. Belg. Math. Soc. Simon Stevin
- Volume 19, Number 4 (2012), 597-632.

### On existence of embeddings for point-line geometries

#### Abstract

We describe a construction of a point-line presheaf on a point-line geometry from a set of presheaves on subspaces of the geometry. Then we combine our construction with theorems of M. Ronan to give a new proof of the fact that all polar spaces of finite rank at least four, and several other Grassmann geometries of spherical buildings, are embeddable in projective spaces.

#### Article information

**Source**

Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 4 (2012), 597-632.

**Dates**

First available in Project Euclid: 23 November 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.bbms/1353695903

**Digital Object Identifier**

doi:10.36045/bbms/1353695903

**Mathematical Reviews number (MathSciNet)**

MR3009024

**Zentralblatt MATH identifier**

1268.51009

**Subjects**

Primary: 51E24: Buildings and the geometry of diagrams

**Keywords**

building incidence geometry Grassmann geometry projective embedding diagram geometry

#### Citation

Kasikova, Anna. On existence of embeddings for point-line geometries. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 4, 597--632. doi:10.36045/bbms/1353695903. https://projecteuclid.org/euclid.bbms/1353695903